Network flow spanners

In this article, motivated by applications of ordinary (distance) spanners in communication networks and to address such issues as bandwidth constraints on network links, link failures, network survivability, etc., we introduce a new notion of flow spanner, where one seeks a spanning subgraph H = (V, E′) of a graph G = (V, E) which provides a ‘good’ approximation of the source‐sink flows in G. We formulate several variants of this problem and investigate their complexities. Special attention is given to the version where H is required to be a tree.